Engineering with Computers

, Volume 20, Issue 4, pp 342–353 | Cite as

Building spacetime meshes over arbitrary spatial domains

  • Jeff Erickson
  • Damrong Guoy
  • John M. Sullivan
  • Alper Üngör
Original article

Abstract

We present an algorithm to construct meshes suitable for spacetime discontinuous Galerkin finite-element methods. Our method generalizes and improves the ‘Tent Pitcher’ algorithm of Üngör and Sheffer. Given an arbitrary simplicially meshed domain X of any dimension and a time interval [0, T], our algorithm builds a simplicial mesh of the spacetime domain X × [0, T], in constant time per element. Our algorithm avoids the limitations of previous methods by carefully adapting the durations of spacetime elements to the local quality and feature size of the underlying space mesh.

Keywords

Wave Speed Discontinuous Galerkin Discontinuous Galerkin Method Space Mesh Cone Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors thank David Bunde, Michael Garland, Shripad Thite, and especially Bob Haber for several helpful comments and discussions. We also thank Shripad Thite for correcting a bug in our proof of Lemma 1. Jeff Erickson supported in part by a Sloan Fellowship and NSF CAREER award CCR-0093348. Damrong Gouy supported in part by DOE grant LLNL B341494. John M Sullivan supported in part by NSF grant DMS-00-71520. Alper Üngör This research was performed while this author was a student at the University of Illinois, with the additional support of a UIUC Computational Science and Engineering Fellowship.

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Copyright information

© Springer-Verlag London Limited 2005

Authors and Affiliations

  • Jeff Erickson
    • 1
  • Damrong Guoy
    • 2
  • John M. Sullivan
    • 3
  • Alper Üngör
    • 4
  1. 1.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbana-ChampaignUSA
  2. 2.Center for Simulation of Advanced Rockets, Computational Science and Engineering ProgramUniversity of Illinois at Urbana-ChampaignUrbana-ChampaignUSA
  3. 3.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbana-ChampaignUSA
  4. 4.Center for Geometric and Biological Computing, Department of Computer ScienceDuke UniversityDurhamUSA

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